An Introduction to Mathematics Curriculum Topic Study SAS Elementary Mathematics Teacher Leadership Academy, Year 1

3 Goals for the CTS Intro Session (Learn about) To develop awareness of Curriculum Topic Study (CTS) as a tool you can use for connecting standards and research on learning to classroom practice. (Practice) To provide guided practice in using CTS. (Apply) To consider ways you might apply CTS to your work.

The CTS Project NSF-funded TPC Professional Development Materials Project awarded to the Maine Mathematics and Science Alliance in partnership with West Ed 2 resources guides: Science and Mathematics Curriculum Topic Study books Facilitator’s Guide to Using Curriculum Topic Study Web Site: www.curriculumtopicstudy.org National Professional Development

What is CTS? A process that incorporates systematic study of standards and research A set of tools and collective resources for improving curriculum, instruction, and assessment An intellectually engaging professional development experience where teachers focus on and discuss student learning

What CTS Is Not CTS IS NOT: A remedy for weak content knowledge (CTS is used to enhance and support content learning) A collection of teaching activities (CTS describes considerations one must take into account when planning or selecting teaching activities) A description of “how to’s” (CTS helps you think through effective teaching based on knowledge of learning goals and how students learn) A quick fix (CTS takes time and dedication to use it effectively) The end-all for professional development (CTS helps you identify additional experiences that will help you grow as a teacher)

Why Use CTS? Clarify and deepen knowledge of relevant curricular topics Develop a common knowledge base and language about standards and research Move beyond personal opinions and assumptions to consider key ideas and practices developed through consensus by the mathematics education community “Stand on the Shoulders of Giants”- Experts at your fingertips 24/7!

Who Uses CTS? Pre-service Teachers Beginning Teachers Experienced Teachers Teacher Leaders, Mentors, and Coaches Professional Developers Pre-Service and Graduate Mathematics Education Faculty Mathematicians Working with K-12 Teacher Education Curriculum Developers Curriculum, Instruction, and Assessment Committees

Having State and National Standards Is Not Enough… What has been missing is a systematic, scholarly, deliberate process to help educators intellectually engage with standards and research on student learning so they can make effective use of them. CTS provides that “Missing Link.”

A First Glance at the CTS Book Pair up at your tables. Open the CTS book at random. With your partner, do a quick scan of the page you opened to. What do you see that provides you with a “preview” of CTS? Mark the page with a sticky note. Repeat 2-3 times to get an initial sense of what is contained in the CTS book. Share an example with the group that particularly interests you and tell why.

Components of a CTS Study Guide CTS Sections and Outcomes Selected Readings from CTS Resources Web Site- Supplementary Material www.curriculumtopicstudy.org See Chapter 2- The CTS Study Guide pp 19- 22

The CTS Guide Each guide has 6 CTS sections (Left Column) Purposes of the sections I : Identify Adult Content Knowledge II : Consider Instructional Implications III : Identify Concepts and Specific Ideas IV : Examine Research on Student Learning V : Examine Coherency and Articulation VI : Clarify State Standards and District Curriculum Each section links to CTS sources and pre-vetted Readings (Right Column)

CTS: The Swiss Army Knife of Curriculum, Instruction, and Assessment Improve adult science literacy (I) Improve knowledge of content teachers teach (I) Examine instructional considerations (II) Identify alternative conceptions (IV) Consider developmental implications (II, IV) Examine scope and sequence (III) See connections within and across topics (V) Clarify state standards and district curriculum (VI) Identify “Big Ideas”, Concepts, Specific Ideas, and Skills (III)

CTS Collective Resources- Experts at Your Fingertips 24/7     Indicates the resource is online

Parallel Resources in Mathematics CTS Getting to Know the Resources Parallel Resources in Mathematics CTS Science Pages 24-26 Science for All Americans Science Matters Benchmarks for Science Literacy The National Science Standards Making Sense of Secondary Science Atlas of Science Literacy Mathematics Pages 27-30 Science for All Americans Beyond Numeracy Benchmarks for Science Literacy Principles and Standards for School Mathematics Research Companion Atlas of Science Literacy

Getting to Know the CTS Resources Divide the 6 resources among your table group. Choose one “expert” for each resource. Read the description of your resource from the CTS book, pp 27-30 Examine the resource, looking for notable features Describe the resource to your table group, pointing out notable features

The CTS Scaffold Scaffold: The structure and supports that a teacher or more knowledgeable helper provides to allow a learner to perform a task he or she cannot yet perform independently. (Vygotsky, 1978; Dixon-Krauss, 1996; Wertsch,1991.)

Quick Summary of the CTS Scaffold STEP 1:Scan and select the CTS category.  STEP 2: Scan the list of topics within the category that include the content you are examining. STEP 3:Select the CTS guide you will use. STEP 4: Determine which section(s) of the CTS guide will help you find the information you need. STEP 5:Select the resource(s) you will use, the grade span(s), and the readings. STEP 6: Examine the reading for information relevant to your topic and task. STEP 7: Record your findings. If you do not find what you need, go back to Step 2 and repeat with another topic.

Quick Scaffold Practice Steps 1-3 “What kinds of experiences should I provide my middle school students with when learning about percent?” Category? Numbers and Operations CTS Topic Guide? Percent Page Number of CTS Guide? Page 129

Quick Scaffold Practice- Step 4 “What kinds of experiences should I provide my middle school students when learning about percent?” Section? Section II Outcome? Consider Instructional Implications

Quick Scaffold Practice- Step 5 “What kinds of experiences should I provide my middle school students when learning about percent?” Which resource, grade level, and page numbers do I read? Benchmarks- Numbers, grade span essay, p 123 and/or NCTM, grades 6-8, Number and Operations, p 215 Understanding Numbers, pp 215-217 What part of the page do I focus on? Just the essay, not the bullets!

More Quick Scaffold Practice Steps 1-3 “What specific ideas about statistics should I focus on at the 3-5 grade level?” Category? Data Analysis CTS Topic Guide? Statistical Reasoning or Summarizing Data Page Number of CTS Guide? Page 186 or 187

More Quick Scaffold Practice- Step 4 “What specific ideas about statistics should I focus on at the 3-5 grade level?” Section? Section III (Could also include Section V and VI) Outcome? Identify Concepts and Specific Ideas

More Quick Scaffold Practice- Step 5 Guide: Statistical Reasoning Which resource, grade level, and page numbers do I read? Benchmarks- 9D Uncertainty pages 227-230; 9E Reasoning pages 232-234; 12E Critical Response Skills pages 298-300 PSSM- 3-5 Data Analysis and Probability page 176 or 400 What part of the page do I focus on? Just the bulleted learning goals, not the essay.

More Quick Scaffold Practice Steps 1-3 “What should adults know about mathematical equations? Category? Algebra CTS Topic Guide? Expressions and Equations Page Number of CTS Guide? Page 136

More Quick Practice- Step 4 “What should adults know about mathematical equations?” Section? Section I Outcome? Identify Adult Content Knowledge

More Quick Scaffold – Step 5 “What should adults know about mathematical equations?” Which resource, grade level, and page numbers do I read? Science for All Americans- Ch 9 pp 132-34 and/or Beyond Numeracy- Algebra, Some Basic Principles, pp 7-9

And Even More Practice- Steps 1-3 “I’m curious to see how the concept and skills related to proportional reasoning develops from elementary grades through high school” Category? Integrated Topics CTS Topic Guide? Proportionality Page Number of CTS Guide? Page 198

And Even More Practice- Step 4 “I’m curious to see how the concept and skill related to proportional reasoning develops from elementary grades through high school” Section? Section V Outcome? Examine Coherency and Articulation

And Even More Practice- Step 5 “I’m curious to see how the concept and skill related to proportional reasoning develops from elementary grades through high school” What strand maps will you use? Ratios and Proportionality Is there a conceptual strand within a map you should focus on? Parts and Wholes, Description or Comparison, and Computation

Last One! “I wonder what difficulties or common misconceptions I should anticipate when students create and interpret graphs?” Category? Integrated Topics CTS Topic Guide? Graphic Representation Page Number of CTS Guide? Page 196

Step 4? “I wonder what difficulties or common misconceptions I should anticipate when students interpret graphs?” Section? Section IV Outcome? Examine Research on Student Learning

Read and Examine Related Parts Students of all ages often interpret graphs of situations as literal pictures rather than as symbolic representations of the situations. Many students interpret distance/time graphs as the paths of actual journeys. In addition, students confound the slope of a graph with the maximum or the minimum value and do not know that the slope of a graph is a measure of rate. When constructing graphs, middle-school and high-school students have difficulties with the notions of interval scale and coordinates even after traditional instruction in algebra. For example, some students think it is legitimate to construct different scales for the positive and the negative parts of the axes. Alternatively, students think that the scales on the X and Y axes must be identical, even if that obscures the relationship. When interpreting graphs, middle-school students do not understand the effect that a scale change would have on the appearance of the graph. Finally, students read graphs point-by-point and ignore their global features. This has been attributed to algebra lessons where students are given questions that they could easily answer from a table of ordered pairs. They are rarely asked questions about maximum and minimum values; intervals over which a function increases, decreases or levels off; or rates of change.

Read and Examine Related Parts Students of all ages often interpret graphs of situations as literal pictures rather than as symbolic representations of the situations. Many students interpret distance/time graphs as the paths of actual journeys. In addition, students confound the slope of a graph with the maximum or the minimum value and do not know that the slope of a graph is a measure of rate. When constructing graphs, middle-school and high-school students have difficulties with the notions of interval scale and coordinates even after traditional instruction in algebra. For example, some students think it is legitimate to construct different scales for the positive and the negative parts of the axes. Alternatively, students think that the scales on the X and Y axes must be identical, even if that obscures the relationship. When interpreting graphs, middle-school students do not understand the effect that a scale change would have on the appearance of the graph. Finally, students read graphs point-by-point and ignore their global features. This has been attributed to algebra lessons where students are given questions that they could easily answer from a table of ordered pairs. They are rarely asked questions about maximum and minimum values; intervals over which a function increases, decreases or levels off; or rates of change.

Accountable Talk (Lauren Resnick, University of Pittsburgh) Involves listening to each other attentively; building on each others’ ideas and respectfully challenging each other; referring regularly to the texts and reading notes; provided evidence for opinions and theories; and asking questions and probing to clarify ideas.

Let’s Get Started! CTS is like learning any new skill. It takes practice, perseverance, focus, and a lot of effort!

CTS Snapshots Practice using the scaffold to answer the questions on your assigned snapshots. Do not take shortcuts on round 1! Record notes from your reading that address the question (not the entire topic). Complete a reflection note. Post your reflection note on the reflection wall before you begin a new snapshot.

Reflection Wall Prompts Pick three snapshot questions that most interest you. Read the answer to those questions.

Reflection Wall Prompts What surprised you about the CTS findings? How did CTS add to what you already knew? How will this information be useful to you in your work? What further questions does this raise for you?

CTS Supporting SAS Read your assigned vignette, either 1, 2, 4, 6, or 8 On chart paper Summarize your vignette Answer the question “How would using CTS, as described in your vignette, complement and enhance your use of SAS?

Examine the Teaching Math for Learning Concept Map in the front of your binder: What connections have you made to SAS through your learning experiences in this academy? Discuss with your table.

Goals for the module Look back over the pedagogical and mathematical goals we have developed from each session Find any pedagogical or mathematical themes Determine overarching goals you have for your district participants Teacher see themselves as mathematical thinkers and learners. Teachers see students as mathematical thinkers and are open to their strategies. Teachers see the value in investigating the practice of teaching. Development of a professional learning community.